Nonlinear Charge Control for a Collinear Fixed-Shape Three-Craft Equilibrium

The collinear equilibrium three-craft-formation charge feedback control problem is investigated. Given a charged-equilibrium collinear configuration of spacecraft flying in deep space, a nonlinear charge feedback control algorithm is developed to stabilize the formation to the desired shape and size. The Coulomb forces are assumed to be acting along the line-of-sight directions between the bodies and thus do not provide general vehicle position controllability. A study of the charged collinear three-craft formation shows that there exists an infinite number of equilibrium charge solutions for any collinear configuration. Given a real value of one spacecraft charge, the required equilibrium charges of the remaining two vehicles are solved analytically. A Lyapunov-based nonlinear control algorithm is developed to stabilize the configuration to the equilibrium state using only the spacecraft charges as the control states. Real charge solutions are ensured by using the one-dimensional solution null-space. Numerical simulations illustrate the new charge feedback control performance. In contrast to earlier efforts, collinear configurations are stabilized even in the presence of very large initial position errors.

[1]  John F. Berryman,et al.  Analytical Charge Analysis for Two- and Three-Craft Coulomb Formations , 2007 .

[2]  Gordon G. Parker,et al.  Reconfiguration of a Nadir-Pointing 2-Craft Coulomb Tether , 2007 .

[3]  Hanspeter Schaub,et al.  Orbit-nadir aligned coulomb tether reconfiguration analysis , 2008 .

[4]  C. Saaj,et al.  Hybrid propulsion system for formation flying using electrostatic forces , 2010 .

[5]  M. S. Gussenhoven,et al.  SCATHA survey of high-level spacecraft charging in sunlight , 1986 .

[6]  Hanspeter Schaub,et al.  Hybrid control of orbit normal and along-track two-craft Coulomb tethers , 2009 .

[7]  R. Olsen,et al.  Importance of differential charging for controlling both natural and induced vehicle potentials on ATS-5 and ATS-6 , 1980 .

[8]  G. Parker,et al.  Study of Interspacecraft Coulomb Forces and Implications for Formation Flying , 2003 .

[9]  J. Bittencourt.  Fundamentals of plasma physics , 1986 .

[10]  Islam I. Hussein,et al.  Stability and control of relative equilibria for the three-spacecraft Coulomb tether problem , 2009 .

[11]  H. Schaub,et al.  Linear Dynamics and Stability Analysis of a Two-Craft Coulomb Tether Formation , 2006 .

[12]  H. Schaub,et al.  Stability and Reconfiguration Analysis of a Circularly Spinning 2-Craft Coulomb Tether , 2007, 2007 IEEE Aerospace Conference.

[13]  John F. Berryman,et al.  Necessary conditions for circularly-restricted static coulomb formations , 2006 .

[14]  Brett J. Streetman,et al.  ELECTROSTATIC FORCES FOR SATELLITE SWARM NAVIGATION AND RECONFIGURATION Final Report , 2006 .

[15]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[16]  H. Schaub,et al.  Analytic Solutions for Equal Mass Four-Craft Static Coulomb Formation , 2008 .

[17]  D. R. Nicholson.  Introduction to Plasma Theory , 1983 .